Looking at doing some flying about. Considering an option that has me arriving via LH at BEG from FRA and returning on the turn to FRA 45 mins later. As a US citizen, will I be able to just stay airside as an international transfer pax? I'm not familiar with the airport and the website was not sufficiently helpful. The segments would be on the same ticket so that should eliminate the need to check in again in BEG.

Yes, no worries. Make sure to check in online in order to have a boarding pass to be safe. As said above, you will be thrown in the departure area. All you need to do is reclear security, which is done directly at the gate (no central security check point). That's it. You will be more then fine. Plus, if it's on one ticket, even if something goes wrong, you booked something "legal" and you should be reprotected. But as the same aircraft will bring you home, even if the flight is delayed, you should be more than fine.